New attitude on sequential Ψ-Caputo differential equations via concept of measures of noncompactness

Abstract

Abstract In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko’s attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples.

Keywords

• Babenko’s attitude
• Measure of noncompactness
• Condensing maps
• Ψ-Caputo derivative